Multipoint Full-Wave Model Order Reduction for Delayed PEEC Models With Large Delays

The increase of operating frequencies requires 3-D electromagnetic (EM) methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D EM methods and model order reduction (MOR) techniques are used to reduce such a high complexity. When signal waveform rise times decrease and the corresponding frequency content increases, or the geometric dimensions become electrically large, time delays must be included in the modeling. A PEEC formulation, which include delay elements called τ PEEC method, becomes necessary and leads to systems of neutral delayed differential equations (NDDE). The reduction of large NDDE is still a very challenging research topic, especially for electrically large structures, where delays among coupled elements cannot be neglected or easily approximated by rational basis functions. We propose a novel model order technique for τ PEEC models that is able to accurately reduce electrically large systems with large delays. It is based on an adaptive multipoint expansion and MOR of equivalent first-order systems. The neutral delayed differential formulation is preserved in the reduced model. Pertinent numerical examples based on τ PEEC models validate the proposed MOR approach.